Question on effects of gravity on light and time

[ShadowKnight]

This is my first post and I have no formal physics background, so please be gently with me.

I'm looking to get a better understanding of the effects of gravity on light and time. From what I've read (if I didn't misunderstand) a gravitational field will bend light to some degree. This in turn could make an object appear smaller to an observer who is further from the gravity field. I also understand that a clock close to the gravity field would appear to run slower then one outside of it. I'd be interested in opinions on the following thought.

Let's take 2 identical twins; exact same height, weight and age. Let's place one twin on the Earth (North pole for arguments sake) and the other on the North pole of the moon. Now let's place an observer at a distance facing the twins and exactly equi-distant between them (seen from above as an equilateral triangle). We know the moon has less gravity then the earth, so here are my questions:

1. Assuming that the equi-distant observer is standing perfectly straight up and down in relation to the twins, would he appear to either of the twins to be leaning, or bending toward or away from the direction of the earth? And by this question I mean would this be caused by the Earth's gravity, light bending due to Earth's gravity, or both?
2. To the observer, assuming he had the ability to accurately measure the twins, would the Earth twin appear smaller then the Moon twin by any margin? If so, how much smaller?
3. Assuming the twins each had an extremely accurate clock with them that was perfectly synched at the beginning of this experiment, would there be a noticeable difference between the clock times when the twins call out their times to each other? (I know there is no such thing as instant signal travel, but for the sake of this question let's ignore that and assume they can instantly compare times with each other).

I'd appreciate any insight because while I find I'm able to understand a lot of this stuff, this is the subject that I can't seem to wrap my brain around very well.
Thanks!

 

[ShadowKnight]

OK, after some extensive reading (Thank you Kip Thorne!) I have discovered the answers to my questions, at least enough for now. I was disappointed to not receive any responses on this post, but in hindsight I see that my question was phrased badly. Many of you may have thought I meant the Earth and moon literally while I was just using them as reference points in my example. Maybe I should have used an example of a neutron star and the Earth instead? In future posts I will make sure I point out when I'm being literal and when I'm using an example.

 

[Daminc]

What did you find out? (Just curious)

 

[ShadowKnight]

I found my answer indirectly reading "Black Holes and Time Warps" by Kip Thorne. Chapter 3 (specifically page 131 of paperback) discusses time dilation due to gravity, or spacetime curvature, on our sun. I have copied a few paragraphs from this page here:

"In the case of the sun, the time warpage is small: At the sun's surface time should flow more slowly by just 2 parts in a million (64 seconds in one year) then far from the sun..."
So this leads me to the answer on my hypothetical twins age difference. Supposing one twin on the sun vs. one on the Earth (rather than my bad analogy of the Earth and moon) than the sun twin would be 64 seconds younger than the Earth twin after 1 year.

This section goes on to describe how light is affected by this:
"Since light's frequency of oscillation is governed by the flow of time at the place where the light is emiited, light emerging from atoms on the star's surface will have a lower frequency when it reaches Earth than light emitted by the same atoms in interstellar space. The frequency will be lowered by precisely the same amount as the flow of time is slowed. A lower frequency means a longer wavelength, so light from the star must be shifted toward the red end of the spectrum by the same amount that time is dilated on the star's surface. At the sun's surface the time dialtion is 2 parts in a million, so the gravitational redshift of light arriving at the Earth from the sun should also be 2 parts in a million."

So, what I still need to figure out; how would the sun twin appear to the Earth twin? Would the sun twin appear smaller in size? Or would he just appear to get more faded (or darker) as the gravitational redshift is increased? To phrase this better - how would the Earth twin percieve of the sun twin if the sun were shrinking down to a white dwarf and the redshift of light was increasing?

 

[Daminc]

Just a guess...wouldn't the frequency be down shifted slightly?

i.e yellows would become more green etc

 

[ShadowKnight]

That's what I percieve from the reading too, but I'm wondering if it would cause other effects aside from color changes (would it even cause color changes?). If the gravity were strong enough than all colors would shift to the radio end of the spectrum and I suppose the twin on the surface of the star would disappear from the Earth twin's observational point of view (with the assumption that he wasn't using a radio telescope or other device to 'see' the radio waves)